Question

An expression is shown below:

f(x) = −16x2 + 22x + 3

Part A: What are the x-intercepts of the graph of the f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.

Answer 1

Part A:

To find the x-intercepts, we have to set f(x) = 0
We'll get
\( -16x^2 + 22x + 3 = 0\)

Do you know how to solve a quadratic equation?
There's a few different ways we can do it :)

Part B:
If we have a function
f(x) = Ax^2 + Bx + C

To find the x-value of the vertex, you have to use the formula
x = -b/2a
To find the y-value of the vertex, plug in that number you just got back into the main equation and solve for y!

Depending on the value of A, we'll either have a maximum or a minimum.
If A > 0 then our parabola opens up and we have a minimum
If A < 0 (that is, it's a negative number) then our parabola opens downward and we have a maximum.

Take a look at the image I've attached to help you visualize it better :)

Answer 2

Whenever you come back and we get done with part A and B, we can then work on part C :)